Damage compensation claims in case of cartels are supposed to increase deterrence, compensate losses and increase efficiency. I show that such claims can instead have adverse effects: If suppliers or buyers of cartelists are compensated in proportion to the profits lost due to the cartel, expected cartel profits can increase. Claims of downstream firms against upstream cartelists who do not monopolize the market increase consumer prices. Suppliers of cartelists can be worse off when eligible to compensation. These results apply also to abuses of dominance and call for a more careful approach towards the private enforcement of competition law.